def get_reduced_nonreduced(self):
r"""
Returns
=======
reduced: list
A list of the reduced monomials
non_reduced: list
A list of the monomials that are not reduced
Definition
==========
A polynomial is said to be reduced in x_i, if its degree (the
maximum degree of its monomials) in x_i is less than d_i. A
polynomial that is reduced in all variables but one is said
simply to be reduced.
"""
divisible = []
for m in self.monomial_set:
temp = []
for i, v in enumerate(self.variables):
temp.append(bool(total_degree(m, v) >= self.degrees[i]))
divisible.append(temp)
reduced = [i for i, r in enumerate(divisible) if sum(r) < self.n - 1]
non_reduced = [
i for i, r in enumerate(divisible) if sum(r) >= self.n - 1
]
return reduced, non_reduced
def get_reduced_nonreduced(self):
r"""
Returns
=======
reduced: list
A list of the reduced monomials
non_reduced: list
A list of the monomials that are not reduced
Definition
==========
A polynomial is said to be reduced in x_i, if its degree (the
maximum degree of its monomials) in x_i is less than d_i. A
polynomial that is reduced in all variables but one is said
simply to be reduced.
"""
divisible = []
for m in self.monomial_set:
temp = []
for i, v in enumerate(self.variables):
temp.append(bool(total_degree(m, v) >= self.degrees[i]))
divisible.append(temp)
reduced = [i for i, r in enumerate(divisible)
if sum(r) < self.n - 1]
non_reduced = [i for i, r in enumerate(divisible)
if sum(r) >= self.n -1]
return reduced, non_reduced
def __init__(self, polynomials, variables):
"""
Parameters
==========
variables: list
A list of all n variables
polynomials : list of SymPy polynomials
A list of m n-degree polynomials
"""
self.polynomials = polynomials
self.variables = variables
self.n = len(variables)
# A list of the d_max of each polynomial.
self.degrees = [total_degree(poly, *self.variables) for poly
in self.polynomials]
self.degree_m = self._get_degree_m()
self.monomials_size = self.get_size()
# The set T of all possible monomials of degree degree_m
self.monomial_set = self.get_monomials_of_certain_degree(self.degree_m)
def __init__(self, polynomials, variables):
"""
Parameters
==========
variables: list
A list of all n variables
polynomials : list of sympy polynomials
A list of m n-degree polynomials
"""
self.polynomials = polynomials
self.variables = variables
self.n = len(variables)
# A list of the d_max of each polynomial.
self.degrees = [total_degree(poly, *self.variables) for poly
in self.polynomials]
self.degree_m = self._get_degree_m()
self.monomials_size = self.get_size()
# The set T of all possible monomials of degree degree_m
self.monomial_set = self.get_monomials_of_certain_degree(self.degree_m)